This is a very helpful paper and provides a good background for
understanding the Nature paper, which I think is quite misleading.

It is curious that the Nature paper consistently uses the term
"superluminal", when their data shows the far more dramatic effect of
a *negative* velocity. A negative velocity is one where the output
comes out before the input went in. It can be considered not just
faster than light, but faster than infinity.

For example, they say, "this means that a light pulse propagating through
the atomic vapour cell appears at the exit side so much earlier than if it
had propagated the same distance in a vacuum that the peak of the pulse
appears to leave the cell before entering it." The comparison here to
vacuum propagation is meaningless. The peak of the pulse *does* appear
to leave the cell before entering it - not just when compared to c, but
independent of any velocity comparisons. Over and over we see the paper
couching results in terms of comparisons to the speed of light, when in
fact they are dealing with results that appear to propagate into the past.

I think the authors are trying to present their results in this way
in order to make them seem less dramatic, and thereby to make their
explanation seem more plausible. They claim that this result is simply
due to classical effects of interference between frequencies. They also
claim (and here they are really wrong) that the shape of the pulse is
preserved.

In fact, as the quant-ph paper referenced above makes clear, the shape
of the pulse is not and cannot be preserved. This becomes especially
obvious if we consider a larger version of the experiment. Instead of
6 cm of gas, let's suppose we could build a chamber 6 meters long.
Now the negative velocity region will be 100 times larger, giving the
pulse a 6 us advance rather than 60 ns. That's the same as the width
of the pulse itself!

The question then immediately arises, if this would really work (as
the Nature paper seems to imply), what would happen if you built a
feedback system which upon receiving the time-advanced pulse, cut off
the transmission of the original pulse, which hasn't even started yet?

The quant-ph paper analyzes essentially this scenario, and unsurprisingly
it shows that nothing bad happens. In fact, the output pulse does
*not* depend on the shape of the input pulse. Rather, it is in effect
*extrapolating* the pulse shape based on the amount of input it has seen
so far. If you try to do the feedback, the change in the input pulse
causes the output pulse to go into a damped oscillation.

Furthermore, the front of the output pulse cannot be superluminally
advanced over the front of the input pulse (the Nature paper does mention
this at the very end, but they don't explain that it contradicts their
earlier explanation of what is happening). This is not very apparent in
the present data, where the acceleration is only about 1% of pulse width,
but if we scale the experiment up, it will become glaringly obvious.
With the 100 fold expanded version of the experiment, there is no way to
have a reasonably shaped pulse which is 6 us advanced over the source, but
which also has its front not advanced at all over the source. What you
will get is a completely misshapen pulse, probably with a rapid rise,
or perhaps some of the nonlinear ringing behavior shown in the quant-ph
paper Scerir references above.

To sum up, in the Nature experiment, the pulse shape can and does
change because the front cannot be advanced. This doesn't show up very
much on their current data but would become obvious if the experiment
were scaled up. The explanation in terms of classical interference
is misleading as it implies that scaling up the experiment would lead
to further advanced pulses, which it would not; it would just lead to
misshapen pulses. The quant-ph paper offers a much more coherent and
lucid explanation of what is going on.